Exporters can claim a refund of IGST paid on exported goods through the GST common portal by filing form GSTR-1 to declare export shipments and the IGST amount. The portal will match the GSTR-1 filing against customs shipping records and automatically refund the IGST amount by debiting the exporter's electronic ledger if no discrepancies are found. Any errors must be rectified in the next GSTR-1 filing.